基于Copula函数的水库防洪安全设计

Safety design for reservoir flood control based on Copula function

在进行水库防洪安全设计时,传统单变量方法均未考虑洪水特征值之间的相关性,有一定的局限性。本文采用二维Copula函数构造年最大洪水峰、量的联合分布,以两变量重现期为防洪标准,选取多组峰、量组合,用以放大典型洪水过程线,经水库调洪演算得到一系列最高水位,最终得到这一系列最高水位的变化范围。以隔河岩水库为例,推求了两变量重现期下调洪最高水位的上限和下限,并与单变量同频率方法所对应的调洪最高水位进行比较,结果表明:单变量同频率方法对应的调洪最高水位处于上限和下限之间,但略小于两变量同频率组合对应的水位,因此,从水库防洪安全角度考虑,采用两变量同频率组合作为设计洪水值更为科学合理。本研究可供水库的防洪设计和安全运行提供参考。

The current method of flood control and safety design for reservoir is based on univariate distribution and it is unable to consider the dependence structure between different flood characteristics. This paper presents a new method to improve the existing one. First, a Copula-based bivariate joint distribution of flood peak and volume is constructed and bivariate return period is used to generate various combinations of the peak and volume. Then, the design flood hydrographs, which are fully characterized by the peak and volume, are routed to determine a series of highest stages in the reservoir caused by its inflow flood, and the variation range of all these stages can be obtained. In a case study of the Geheyan reservoir on the Qing River, upper and lower bounds of the highest stages under the bivariate return period were determined and compared with those by a univariate method using the same frequency. The results show that the calculations of highest stages by univariate design fall within the two bounds, but slightly less than those by bivariate design. For design of reservoir flood control, this study suggests that the bivariate distribution gives more safe results.